Sequential multiple-break procedures for nonlinear multivariate and panel models
Develop sequential sup-F-type or analogous tests and associated asymptotic theory for detecting and estimating multiple structural breaks in nonlinear multivariate regression models and nonlinear panel data models, extending beyond single-equation nonlinear least squares settings.
References
For nonlinear multivariate and panel data models, equivalent procedures are not currently available to the best of our knowledge.
Several extensions remain open. First, the present formal theory concerns a single change. Recursive, interval-based, or penalized segmentation provides a natural route to multiple-change analysis, but uniform recovery guarantees for the resulting procedure require separate theoretical development. Second, the vocabulary dimension and retained projection dimensions are treated as fixed. A growing-vocabulary theory would require dimension-dependent concentration, degree-stability conditions, and control of the pilot projection maps. Third, oracle equivalence requires the finite-document representation error to vanish sufficiently quickly relative to the number of time periods. A noise-aware limit theory is needed when finite-document error remains first-order rather than asymptotically negligible. Fourth, the present default WCO targets linear cross-view covariance. Developing and calibrating a richer family of nonlinear concordance operators could extend diagnostic sensitivity while preserving a clear population interpretation. Finally, extending the framework from offline analysis to sequential monitoring, in the spirit of \citet{Xie2013} and \citet{Leung2017}, is an important direction for future work.